Political scientists Nicholas O. Stephanopoulos, Eric M. McGhee, and Steven Rogers, have posted “The Realities of Electoral Reform” at this link. Click on the “download” button. The study uses data on voter preferences by legislative and congressional district to determine whether various kinds of election laws improve or worsen the fit between public opinion in a district and the behavior of that district’s representatives. The assumption is that it is desirable that the voting behavior of state legislators and members of Congress ought to match public opinion in his or her district or state.

Page 38 of the study presents the data for various kinds of primary system. The data shows that there is a better fit between public opinion in a district, and the representative chosen by that district, in closed primary states than in open primary and top-two primary states. Thanks to Rick Hasen for the link.